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Question 7 The mean time taken by all participants to run a road race was found to be 150 minutes with a standard deviation of 10 minutes. Using Chebyshevs theorem, find the percentage of runners who ran this road race in 120 to 180 minutes. Round your answer to the nearest integer the tolerance is +/-2%
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Answer #1

By Chebyshev's inequality, we know

Prleft ( |X-mu|leq ksigma ight )=1-{1over k^2}

Since 120-150-3 × 10 and 180-150 3 × 10 ,

So

Pr( 120 < X < 180) Pr (X-150| < 2 × 10) 32 0,888

Hence the required probability is 88.89%

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